where \(\tilde{\mathbf {T}}\)  in the form of Eq. () is one part of \(\tilde{\mathbf {U}}\) .
Note in passing that, given the simplicity of the chosen AOs, the pre-LMOs (REF ) can also be obtained by a top-down localization[1]} of the pre-CMOs (REF ) via, e.g., the Pipek and Mezey (PM) scheme[2]}. In this case, the OAOs can be obtained simply by a one-step symmetric orthonormalization of all the AOs,
without the need of classifying their occupations. Instead, the singly occupied pre-CMOs can readily
be determined before the top-down localization is executed, since they should overlap most with the singly occupied molecular CMOs
(cf. Eqs. (REF ) and (REF )).
